×

Einstein equation for an invariant metric on generalized flag manifolds and inner automorphisms. (English) Zbl 0936.53031

Author’s abstract: “A generalized flag manifold is a homogeneous space \(G/K\) whose isotropy subgroup \(K\) is the centralizer of a torus in \(G\). We show that the Einstein equation for a \(G\)-invariant metric on \(G/K\) is invariant under the group of inner automorphisms of the Lie algebra of \(G\) that preserve the Lie algebra of \(K\) and a fixed Cartan subalgebra of \(K\)”.

MSC:

53C30 Differential geometry of homogeneous manifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
PDFBibTeX XMLCite
Full Text: EuDML EMIS